Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1181 |
| commutator, socle | C22×C29 | C22×C4 |
| Fitting, prime radical | C2×D4×C29 | C4 |
| cosocle | C2×Dic29 | C23 |
| hypercenter | C2×D4 | #1181 |
| hypocenter | C29 | #435 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90800 | C2 | semidirect |
| 2. C22×#6599 | C2 | semidirect |
| 4. C22⋊#6599 | C2 | semidirect |
| 5. C22⋊#6599 | C2 | semidirect |
| 6. #11745220 | C2 | semidirect |
| 7. #11745218 | C2 | semidirect |
| 36. #6599 | D4 | semidirect |
| 42. C22×C29 | M16 | semidirect |
| 63. C29 | #435 | semidirect |
| 98. C22 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90800 | 2 |
| C22×#6599 | 2 |
| D4×Dic29 | 2 |
| C22⋊#6599 | 2 |
| #11745220 | 2 |
| #11745218 | 2 |
| #435 | 29 |